Division of fractions by decimals

Division of fractions by decimals

Decimals are fractions of 10 written by using a point (.) which separates a whole number and a fraction of 10 and its multiples. For example, $1/10$ is written in decimals as $0.1$, $1/100$ as $0.01$, $1/1000$ as $0.001$, $3/10$ as $0.3$, and $79/100$ as $0.79$.

Also, mixed numbers can be written as decimals. For example, $5\ 5/10$ can be written in decimals as $5.5$, $1\ 34/100$ as $1.34$, and $61\ 782/1000$ as $61.782$.

When dividing fractions by decimals, first, convert the decimals into fractions, and then follow the procedures of dividing fractions by fractions using the formula $a/b \div c/d = a/b \times d/c$.

Example 1

$1/10 \div 0.3 =$

Solution

Convert $0.3$ into fraction:

$0.3 = 3/10$.

Thus, $1/10 \div 0.3 = 1/10 \div 3/10$.

Using the formula $a/b \div c/d = a/b \times d/c$:

$1/10 \div 0.3 = 1/10 \times 10/3 = 1/3.$

Therefore, $1/10 \div 0.3 = 1/3$.

Example 2

$5/8 \div 0.125 =$

Solution

Change $0.125$ into fraction:

$0.125 = 125/1000$.

Thus, $5/8 \div 0.125 = 5/8 \div 125/1000$.

Using the formula $a/b \div c/d = a/b \times d/c$:

$5/8 \div 125/1000 = 5/8 \times 1000/125 = 5.$

Therefore, $5/8 \div 0.125 = 5$.

Example 3

$750/15000 \div 10.15 =$

Solution

Change $10.15$ into fraction:

$10.15 = 10\ 15/100 = 1015/100$.

Thus, $750/15000 \div 10.15 = 750/15000 \div 1015/100$.

$750/15000 \div 1015/100 = 750/15000 \times 100/1015 = 5/1015 = 1/203.$

Therefore, $750/15000 \div 10.15 = 1/203$.